{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:MSHRRQFCNXG6V7WIRCQQOPM5N4","short_pith_number":"pith:MSHRRQFC","schema_version":"1.0","canonical_sha256":"648f18c0a26dcdeafec888a1073d9d6f3a9424c130b9dcef93ddd05eac2fc7d0","source":{"kind":"arxiv","id":"2406.01533","version":1},"attestation_state":"computed","paper":{"title":"Coprime-Universal Quadratic Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giacomo Cherubini, Matteo Bordignon","submitted_at":"2024-06-03T17:05:18Z","abstract_excerpt":"Given a prime $p>3$, we characterize positive-definite integral quadratic forms that are coprime-universal for $p$, i.e. representing all positive integers coprime to $p$. This generalizes the $290$-Theorem by Bhargava and Hanke and extends later works by Rouse ($p=2$) and De Benedetto and Rouse ($p=3$). When $p=5,23,29,31$, our results are conditional on the coprime-universality of specific ternary forms. We prove this assumption under GRH (for Dirichlet and modular $L$-functions), following a strategy introduced by Ono and Soundararajan, together with some more elementary techniques borrowed"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2406.01533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-06-03T17:05:18Z","cross_cats_sorted":[],"title_canon_sha256":"78a3fc4a2e423f08020eb04397c746fb3e832644529644d66104fcde0aebcb48","abstract_canon_sha256":"1a73c35a8fb6abea7b8705042c1ad557b7cbcfd2515b7157f0d5376ffa7d9c4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:40.809742Z","signature_b64":"ULc/IpTL05VOoL5GMNrDUpOOYu087bUUxxg7s4UoHB/whgQpZrvTEw1ZyAqTCZKXPIyceKx8fpqaibTNVQ3JCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"648f18c0a26dcdeafec888a1073d9d6f3a9424c130b9dcef93ddd05eac2fc7d0","last_reissued_at":"2026-07-05T08:26:40.809285Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:40.809285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coprime-Universal Quadratic Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giacomo Cherubini, Matteo Bordignon","submitted_at":"2024-06-03T17:05:18Z","abstract_excerpt":"Given a prime $p>3$, we characterize positive-definite integral quadratic forms that are coprime-universal for $p$, i.e. representing all positive integers coprime to $p$. This generalizes the $290$-Theorem by Bhargava and Hanke and extends later works by Rouse ($p=2$) and De Benedetto and Rouse ($p=3$). When $p=5,23,29,31$, our results are conditional on the coprime-universality of specific ternary forms. We prove this assumption under GRH (for Dirichlet and modular $L$-functions), following a strategy introduced by Ono and Soundararajan, together with some more elementary techniques borrowed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01533","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.01533/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2406.01533","created_at":"2026-07-05T08:26:40.809343+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.01533v1","created_at":"2026-07-05T08:26:40.809343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01533","created_at":"2026-07-05T08:26:40.809343+00:00"},{"alias_kind":"pith_short_12","alias_value":"MSHRRQFCNXG6","created_at":"2026-07-05T08:26:40.809343+00:00"},{"alias_kind":"pith_short_16","alias_value":"MSHRRQFCNXG6V7WI","created_at":"2026-07-05T08:26:40.809343+00:00"},{"alias_kind":"pith_short_8","alias_value":"MSHRRQFC","created_at":"2026-07-05T08:26:40.809343+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.19371","citing_title":"Kitaoka's Conjecture for quadratic fields","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4","json":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4.json","graph_json":"https://pith.science/api/pith-number/MSHRRQFCNXG6V7WIRCQQOPM5N4/graph.json","events_json":"https://pith.science/api/pith-number/MSHRRQFCNXG6V7WIRCQQOPM5N4/events.json","paper":"https://pith.science/paper/MSHRRQFC"},"agent_actions":{"view_html":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4","download_json":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4.json","view_paper":"https://pith.science/paper/MSHRRQFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.01533&json=true","fetch_graph":"https://pith.science/api/pith-number/MSHRRQFCNXG6V7WIRCQQOPM5N4/graph.json","fetch_events":"https://pith.science/api/pith-number/MSHRRQFCNXG6V7WIRCQQOPM5N4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4/action/storage_attestation","attest_author":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4/action/author_attestation","sign_citation":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4/action/citation_signature","submit_replication":"https://pith.science/pith/MSHRRQFCNXG6V7WIRCQQOPM5N4/action/replication_record"}},"created_at":"2026-07-05T08:26:40.809343+00:00","updated_at":"2026-07-05T08:26:40.809343+00:00"}